1. The problem asks for the number of elements in the set $ (X \cup Y) - (X \cap Y) $ where $ X = \{1,2,3\} $ and $ Y = \{2,3,4\} $. 2. First, find the union $ X \cup Y $, which includes all elements in either $X$ or $Y$: $$ X \cup Y = \{1,2,3,4\} $$ 3. Next, find the intersection $ X \cap Y $, which includes elements common to both $X$ and $Y$: $$ X \cap Y = \{2,3\} $$ 4. Now, subtract the intersection from the union: $$ (X \cup Y) - (X \cap Y) = \{1,2,3,4\} - \{2,3\} = \{1,4\} $$ 5. Count the number of elements in the resulting set: $$ |\{1,4\}| = 2 $$ 6. Therefore, the number of elements in the set $ (X \cup Y) - (X \cap Y) $ is 2.